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   <h4 class="subsectionHead"><span class="titlemark">3.3   </span> <a 
 id="x23-770003.3"></a>3D Elements</h4>
<!--l. 1692--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">3.3.1   </span> <a 
 id="x23-780003.3.1"></a>Tetrah1ht - tetrahedral 3D element</h5>
<!--l. 1693--><p class="noindent" >Represents isoparametric four-node tetrahedral element. Each node has 1 degree of freedom. The same
numbering convection is adopted as in mechanics, see Fig.&#x00A0;<a 
href="elementlibmanualsu8.html#x13-4600114">14<!--tex4ht:ref: lintetrahedron_fig --></a>. The element features are summarized in
Table&#x00A0;<a 
href="#x23-7800152">52<!--tex4ht:ref: Tetrah1htsummary --></a>.
<div class="center" 
>
<!--l. 1696--><p class="noindent" >
<div class="table">
<!--l. 1696--><p class="noindent" ><a 
 id="x23-7800152"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-54" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-54-1g"><col 
id="TBL-54-1"></colgroup><colgroup id="TBL-54-2g"><col 
id="TBL-54-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-54-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-54-1-2"  
class="td11"><!--l. 1696--><p class="noindent" ><span 
class="cmbx-10">Tetrah1ht</span>                                                      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-54-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-54-2-2"  
class="td11"><!--l. 1696--><p class="noindent" >Isoparametric,  four-node  tetrahedral  element  with  linear
approximation for heat transfer problems                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-54-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-54-3-2"  
class="td11"><!--l. 1696--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-54-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-54-4-2"  
class="td11"><!--l. 1697--><p class="noindent" ><span 
class="cmtt-10">NIP</span>: allows to change the default number of integration
point used.                                                              </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-54-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-54-5-2"  
class="td11"><!--l. 1698--><p class="noindent" >Single dof (T_f - temperature) is required in each node.    </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-54-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-54-6-2"  
class="td11"><!--l. 1699--><p class="noindent" >Linear approximation of temperature.                           </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-54-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-54-7-2"  
class="td11"><!--l. 1702--><p class="noindent" >Integration  using  gauss  integration  formula  in  1  (the
default),  or  4  integration  points.  The  default  number
of  integration  point  used  can  be  overloaded  using  <span 
class="cmtt-10">NIP</span>
parameter.                                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-54-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-8-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-54-8-2"  
class="td11"><!--l. 1705--><p class="noindent" >Body loads are supported. Boundary loads are supported
and computed using numerical integration. The side and
surface numbering is shown in Fig.&#x00A0;<a 
href="elementlibmanualsu8.html#x13-4600114">14<!--tex4ht:ref: lintetrahedron_fig --></a>.                          </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-54-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-9-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-54-9-2"  
class="td11"><!--l. 1706--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-54-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-10-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-54-10-2"  
class="td11"><!--l. 1707--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-54-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-11-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-54-11-2"  
class="td11"><!--l. 1709--><p class="noindent" >                                                 </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-54-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-12-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-54-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-54-13-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;52: </span><span  
class="content">Tetrah1ht element summary</span></div><!--tex4ht:label?: x23-7800152 -->
</div><hr class="endfloat" />
</div>
</div>
<!--l. 1712--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">3.3.2   </span> <a 
 id="x23-790003.3.2"></a>Brick1ht - hexahedral 3D element</h5>
<!--l. 1714--><p class="noindent" >Represents isoparametric eight-node brick/hexahedron finite element for heat transfer problems. Each node has 1
degree of freedom. The element features are summarized in Table&#x00A0;<a 
href="#x23-7900253">53<!--tex4ht:ref: Brick1htsummary --></a>.
<!--l. 1717--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x23-7900123"></a>
                                                                                           
                                                                                           
<!--l. 1--><p class="noindent" ><img 
src="elementlibmanual-figure25.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;23: </span><span  
class="content">Brick1ht element. Node numbers are in black, side numbers are in blue, and surface numbers are
in red.</span></div><!--tex4ht:label?: x23-7900123 -->
                                                                                           
                                                                                           
<!--l. 1725--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1727--><p class="noindent" >
<div class="table">
<!--l. 1727--><p class="noindent" ><a 
 id="x23-7900253"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-55" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-55-1g"><col 
id="TBL-55-1"></colgroup><colgroup id="TBL-55-2g"><col 
id="TBL-55-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-55-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-55-1-2"  
class="td11"><!--l. 1727--><p class="noindent" ><span 
class="cmbx-10">Brick1ht</span>                                                        </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-55-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-55-2-2"  
class="td11"><!--l. 1727--><p class="noindent" >Isoparametric,
hexahedral 3D element with linear approximation for heat
transfer problems                                                      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-55-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-55-3-2"  
class="td11"><!--l. 1727--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-55-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-55-4-2"  
class="td11"><!--l. 1728--><p class="noindent" ><span 
class="cmtt-10">NIP</span>: allows to change the default number of integration
point used.                                                              </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-55-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-55-5-2"  
class="td11"><!--l. 1729--><p class="noindent" >Single dof (T_f - temperature) is required in each node.    </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-55-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-55-6-2"  
class="td11"><!--l. 1730--><p class="noindent" >Linear approximation of temperature.                           </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-55-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-55-7-2"  
class="td11"><!--l. 1733--><p class="noindent" >Integration  using  gauss  integration  formula  in  8  (the
default),  or  27  integration  points.  The  default  number
of  integration  point  used  can  be  overloaded  using  <span 
class="cmtt-10">NIP</span>
parameter.                                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-55-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-8-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-55-8-2"  
class="td11"><!--l. 1736--><p class="noindent" >Body loads are supported. Boundary loads are supported
and computed using numerical integration. The side and
surface numbering is shown in fig. (<a 
href="#x23-7900123">23<!--tex4ht:ref: Brick1htfig --></a>)).                        </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-55-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-9-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-55-9-2"  
class="td11"><!--l. 1737--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-55-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-10-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-55-10-2"  
class="td11"><!--l. 1738--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-55-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-11-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-55-11-2"  
class="td11"><!--l. 1740--><p class="noindent" >                                                 </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-55-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-12-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-55-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-55-13-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;53: </span><span  
class="content">Brick1ht element summary</span></div><!--tex4ht:label?: x23-7900253 -->
</div><hr class="endfloat" />
</div>
</div>
   <h5 class="subsubsectionHead"><span class="titlemark">3.3.3   </span> <a 
 id="x23-800003.3.3"></a>Brick1hmt - hexahedral 3D element</h5>
<!--l. 1743--><p class="noindent" >Represents isoparametric eight-node quadrilateral finite element for heat and mass (one constituent) transfer
problems. Two dofs (T_f - temperature and C_1 - concentration) are required in each node. Linear
approximation of temperature and mass concentration. Other features are similar to Brick1 element, see section
<a 
href="#x23-790003.3.2">3.3.2<!--tex4ht:ref: Brick1ht --></a>.
<!--l. 1750--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">3.3.4   </span> <a 
 id="x23-810003.3.4"></a>QBrick1ht - quadratic hexahedral 3D element</h5>
<!--l. 1751--><p class="noindent" >Implementation of quadratic 3d 20-node finite element. Each node has 1 degree of freedom. See section &#x00A0;<a 
href="elementlibmanualsu8.html#x13-450002.8.3">2.8.3<!--tex4ht:ref: QSpace_element --></a> for node
numbering order and order of faces. The element features are summarized in Table&#x00A0;<a 
href="#x23-8100154">54<!--tex4ht:ref: QBrick1htsummary --></a>.
<div class="center" 
>
<!--l. 1755--><p class="noindent" >
<div class="table">
                                                                                           
                                                                                           
<!--l. 1755--><p class="noindent" ><a 
 id="x23-8100154"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-56" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-56-1g"><col 
id="TBL-56-1"></colgroup><colgroup id="TBL-56-2g"><col 
id="TBL-56-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-56-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-56-1-2"  
class="td11"><!--l. 1755--><p class="noindent" ><span 
class="cmbx-10">QBrick1ht</span>                                                     </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-56-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-56-2-2"  
class="td11"><!--l. 1755--><p class="noindent" >Isoparametric,  hexahedral  3D  element  with  quadratic
approximation for heat transfer problems                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-56-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-56-3-2"  
class="td11"><!--l. 1755--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-56-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-56-4-2"  
class="td11"><!--l. 1756--><p class="noindent" ><span 
class="cmtt-10">NIP</span>: allows to change the default number of integration
point used, possible values are 8, 27 (default) and 64.       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-56-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-56-5-2"  
class="td11"><!--l. 1757--><p class="noindent" >Single dof (T_f - temperature) is required in each node.    </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-56-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-56-6-2"  
class="td11"><!--l. 1759--><p class="noindent" >Quadratic approximation of temperature and geometry..   </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-56-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-56-7-2"  
class="td11"><!--l. 1762--><p class="noindent" >Integration  using  gauss  integration  formula  in  8,  27
(default),  or  64  integration  points.  The  default  number
of  integration  point  used  can  be  overloaded  using  <span 
class="cmtt-10">NIP</span>
parameter.                                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-56-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-8-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-56-8-2"  
class="td11"><!--l. 1763--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-56-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-9-1"  
class="td11">Features </td> <td  style="white-space:wrap; text-align:left;" id="TBL-56-9-2"  
class="td11"><!--l. 1764--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-56-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-10-1"  
class="td11">CS properties       </td><td  style="white-space:wrap; text-align:left;" id="TBL-56-10-2"  
class="td11"><!--l. 1765--><p class="noindent" >-                                                                            </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-56-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-11-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-56-11-2"  
class="td11"><!--l. 1767--><p class="noindent" >                                                 </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-56-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-12-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-56-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-56-13-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;54: </span><span  
class="content">QBrick1ht element summary</span></div><!--tex4ht:label?: x23-8100154 -->
</div><hr class="endfloat" />
</div>
</div>
<!--l. 1769--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">3.3.5   </span> <a 
 id="x23-820003.3.5"></a>QBrick1hmt - quadratic hexahedral 3D element</h5>
<!--l. 1770--><p class="noindent" >The same element as QBrick1ht for heat and mass (one constituent) transfer problems. Two dofs (T_f - temperature
and C_1 - concentration) are required in each node. Linear approximation of temperature and mass concentration.
Other features are similar to QBrick1ht element, see section <a 
href="#x23-810003.3.4">3.3.4<!--tex4ht:ref: QBrick1ht_element --></a>.
                                                                                           
                                                                                           
   <!--l. 1779--><div class="crosslinks"><p class="noindent">[<a 
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